Time Limit: 2000 MS    Memory Limit: 65536 K 


For 2 non-negative integers x and y, f(x, y) is defined as the number of different bits in the binary format of x and y. For example, f(2, 3)=1,f(0, 3)=2, f(5, 10)=4. Now given 2 sets of non-negative integers A and B, for each integer b in B, you should find an integer a in A such that f(a, b) is minimized. If there are more than one such integer in set A, choose the smallest one.


The first line of the input is an integer T (0 < T 100), indicating the number of test cases. The first line of each test case contains 2 positive integers m and n (0 < m, n 100), indicating the numbers of integers of the 2 sets A and B, respectively. Then follow (m + n) lines, each of which contains a non-negative integers no larger than 1000000. The first m lines are the integers in set A and the other n lines are the integers in set B.


For each test case you should output n lines, each of which contains the result for each query in a single line.

Sample Input

2 2 5 1 2 1 2 3 4 5 5 2 1000000 9999 1423 3421 0 13245 353

Sample Output

1 2 1 1 1 9999 0


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